Speed and Velocity
Uniform circular motion is the motion of an object in a circle with a constant speed. The average speed can be calculated by dividing circumference of a circle by the time it takes for one revolution (period). The magnitude of velocity remains constant, but the direction changes and is tangential to the circular path.
Acceleration
Objects moving in a circle at constant speed are accelerating because the direction of velocity is changing. They accelerate towards the center of the circle. The acceleration is dependent on the velocity change and points in the same direction as the velocity change, and it can be measure using an accelerometer.
The Centripetal Force Requirement
There must be an inward force acting upon on object causing an inward acceleration for it to be moving in a circle. Otherwise, the object will continue on a straight path of motion because of inertia. A centripetal force is any force that pushes or pulls the object towards the center of the circle. The force can accelerate the object by changing its direction but cannot change it speed.
Centrifugal Forces
A Centrifugal force pushes or pulls an object away from the center of the circle. However, circular motion does not include outward forces. There is a centripetal force requirement, so there must be an inward force. The outward force that many people think exists in circular motion is really just caused by the tendency of an object to keep moving in its path of motion until another force changes its motion; it is really an inward force keeping the object moving in circular motion.
Mathematics of Circular Motion
The three main quantities that are used to analyze the motion of objects in circles are speed, acceleration, and force. The net force is directed inwards and is related to the acceleration. The equations for the three quantities can be used to solved various types of problems. Average speed = 2*pi*R / T Acceleration = v2 / R Net force = mv2 / R
Lesson 2
Method 2b
12/22/11
1) I understand Newton's 2nd law and how to use it. The acceleration of an object is inversely proportional to the mass of the object and directly proportional to the net force acting on the object. I also understand how roller coasters apply to circular motion. The direction of the acceleration vector of a person on a roller coaster is directed primarily towards the center of the circle.
2) I was confused as to how the different concepts could be applied to a roller coaster situation with the information that we know. I now understand because the acceleration for an object in circular motion is the velocity squared divided by the radius. You can solve problems using a FBD and F=ma equations.
3) I do not have any questions about this section.
4)
I found it interesting how you can calculate the minimum speed needed to get over a loop on a roller coaster or the maximum speed a person can handle on the way down so simply. I've been to amusement parks before but never thought about all of the physics that goes into creating all of the rides.
Lesson 3
Method 2a
1/3/12
1) I understood Kepler's ideas from class discussion. The paths of planets are elliptical in shape with the center of the sun being at one focus. Also, a planet carves out equal areas in equal intervals of time if lines are drawn to the sun. I also understand how Fg=(Gm1m2)/d2 can be used to calculate the force of and acceleration due to gravity.
2) I now more clearly understand the difference between the force of gravity and the acceleration of gravity. I used to refer to them as the same thing. The force of gravity is the actual force, while the acceleration of gravity (g) is the acceleration experienced by an object when the only force acting upon it is the force of gravity, which is the same for all objects.
3) I understand everything that I read.
4) Everything I read was discussed during class.
Lesson 2
Method 2a
The Clockwork Universe, parts 1-4
1/4/12
1) I understood Kepler's idea of the sun being at one focus of the elliptical orbit of planets. I also understood how the heliocentric model of the solar system cam about and debunked the previous belief that everything orbited around the earth. Copernicus introduced the new idea, which was not accepted so easily.
The Keplerian system in which a planet follows an elliptical orbit with the Sun at one focus of the ellipse
2) I am now more familiar with Newton. I get that he did no concentrate so much on motion as he did on deviation from steady motion (when an object speeds up, slows down, or changes direction). Newton looked for a cause whenever this deviation happened and described a cause as a force.
3) I understand everything that I read.
4) We did not discuss Rene Descartes in class. He used a two-dimensional coordinate system to locate the position of any point in terms of x and y. This was the beginning of coordinate geometry, representing geometrical shapes with equations.
Lesson 4a-c
Method 2a
1/6/12
1) Kepler's second law basically says that a planet travels faster when it is closer to the sun. This is because a planet sweeps out equal areas in equal amounts of time.
I also understand that the law of harmonies says that that ratio of the period squared to the radius cubed is constant. This ratio is the shown to be the same for all planets.
2) I was confused and didn't understand how things like satellites and moons are really falling. The reading cleared this up and I now get how these things are like projectiles traveling at a large enough velocity that they fall around a planet instead of into it. This is because of the force of gravity acting on things around it.
3) I understand everything I read.
4) Everything I read was discussed during class. One thing that was worded a little differently and is worth mentioning is that the speed, acceleration, and period of an orbiting satellite do not depend on the mass of the satellite.
Lesson 4d-e
Method 2a
1/9/12
1) I understand that weightlessness is a sensation achieved when there are no contact forces. Basically, there is nothing opposing the force of your weight.
Also, a scale does not measure your weight, it measures the upward force applied to your body. A person's mass remains the same, but his or her apparent weight may change on an elevator of different accelerations.
2) The reading clears up how Earth-orbiting astronauts are weightless for the same reasons that riders of a free-falling amusement park ride are weightless. It is because there is no external contact force pushing or pulling upon their body. Gravity is the only force acting upon their body. Being an action-at-a-distance force, it cannot be felt and therefore would not provide any sensation of their weight. It is the force of gravity that supplies the centripetal force requirement to allow the inward acceleration that is characteristic of circular motion.
3) I understand everything that I read.
4) We did not talk about how the total amount of mechanical energy of a satellite in elliptical motion remains constant. Since the only force doing work upon the satellite is an internal (conservative) force, the work done by external forces is zero and mechanical energy is conserved. Unlike the case of circular motion, the energy of a satellite in elliptical motion will change forms. The force of gravity does work upon a satellite to slow it down as it moves away from the earth and to speed it up as it moves towards the earth. If the speed is changing, the kinetic energy will also be changing.
Table of Contents
Lesson 1
Method 512/13/11
Speed and Velocity
Uniform circular motion is the motion of an object in a circle with a constant speed. The average speed can be calculated by dividing circumference of a circle by the time it takes for one revolution (period). The magnitude of velocity remains constant, but the direction changes and is tangential to the circular path.
Acceleration
Objects moving in a circle at constant speed are accelerating because the direction of velocity is changing. They accelerate towards the center of the circle. The acceleration is dependent on the velocity change and points in the same direction as the velocity change, and it can be measure using an accelerometer.
The Centripetal Force Requirement
There must be an inward force acting upon on object causing an inward acceleration for it to be moving in a circle. Otherwise, the object will continue on a straight path of motion because of inertia. A centripetal force is any force that pushes or pulls the object towards the center of the circle. The force can accelerate the object by changing its direction but cannot change it speed.
Centrifugal Forces
A Centrifugal force pushes or pulls an object away from the center of the circle. However, circular motion does not include outward forces. There is a centripetal force requirement, so there must be an inward force. The outward force that many people think exists in circular motion is really just caused by the tendency of an object to keep moving in its path of motion until another force changes its motion; it is really an inward force keeping the object moving in circular motion.
Mathematics of Circular Motion
The three main quantities that are used to analyze the motion of objects in circles are speed, acceleration, and force. The net force is directed inwards and is related to the acceleration. The equations for the three quantities can be used to solved various types of problems.
Average speed = 2*pi*R / T
Acceleration = v2 / R
Net force = mv2 / R
Lesson 2
Method 2b12/22/11
1) I understand Newton's 2nd law and how to use it. The acceleration of an object is inversely proportional to the mass of the object and directly proportional to the net force acting on the object. I also understand how roller coasters apply to circular motion. The direction of the acceleration vector of a person on a roller coaster is directed primarily towards the center of the circle.
2) I was confused as to how the different concepts could be applied to a roller coaster situation with the information that we know. I now understand because the acceleration for an object in circular motion is the velocity squared divided by the radius. You can solve problems using a FBD and F=ma equations.
3) I do not have any questions about this section.
4)
I found it interesting how you can calculate the minimum speed needed to get over a loop on a roller coaster or the maximum speed a person can handle on the way down so simply. I've been to amusement parks before but never thought about all of the physics that goes into creating all of the rides.
Lesson 3
Method 2a1/3/12
1) I understood Kepler's ideas from class discussion. The paths of planets are elliptical in shape with the center of the sun being at one focus. Also, a planet carves out equal areas in equal intervals of time if lines are drawn to the sun. I also understand how Fg=(Gm1m2)/d2 can be used to calculate the force of and acceleration due to gravity.
2) I now more clearly understand the difference between the force of gravity and the acceleration of gravity. I used to refer to them as the same thing. The force of gravity is the actual force, while the acceleration of gravity (g) is the acceleration experienced by an object when the only force acting upon it is the force of gravity, which is the same for all objects.
3) I understand everything that I read.
4) Everything I read was discussed during class.
Lesson 2
Method 2aThe Clockwork Universe, parts 1-4
1/4/12
1) I understood Kepler's idea of the sun being at one focus of the elliptical orbit of planets. I also understood how the heliocentric model of the solar system cam about and debunked the previous belief that everything orbited around the earth. Copernicus introduced the new idea, which was not accepted so easily.
2) I am now more familiar with Newton. I get that he did no concentrate so much on motion as he did on deviation from steady motion (when an object speeds up, slows down, or changes direction). Newton looked for a cause whenever this deviation happened and described a cause as a force.
3) I understand everything that I read.
4) We did not discuss Rene Descartes in class. He used a two-dimensional coordinate system to locate the position of any point in terms of x and y. This was the beginning of coordinate geometry, representing geometrical shapes with equations.
Lesson 4a-c
Method 2a1/6/12
1) Kepler's second law basically says that a planet travels faster when it is closer to the sun. This is because a planet sweeps out equal areas in equal amounts of time.
I also understand that the law of harmonies says that that ratio of the period squared to the radius cubed is constant. This ratio is the shown to be the same for all planets.
2) I was confused and didn't understand how things like satellites and moons are really falling. The reading cleared this up and I now get how these things are like projectiles traveling at a large enough velocity that they fall around a planet instead of into it. This is because of the force of gravity acting on things around it.
3) I understand everything I read.
4) Everything I read was discussed during class. One thing that was worded a little differently and is worth mentioning is that the speed, acceleration, and period of an orbiting satellite do not depend on the mass of the satellite.
Lesson 4d-e
Method 2a1/9/12
1) I understand that weightlessness is a sensation achieved when there are no contact forces. Basically, there is nothing opposing the force of your weight.
Also, a scale does not measure your weight, it measures the upward force applied to your body. A person's mass remains the same, but his or her apparent weight may change on an elevator of different accelerations.
2) The reading clears up how Earth-orbiting astronauts are weightless for the same reasons that riders of a free-falling amusement park ride are weightless. It is because there is no external contact force pushing or pulling upon their body. Gravity is the only force acting upon their body. Being an action-at-a-distance force, it cannot be felt and therefore would not provide any sensation of their weight. It is the force of gravity that supplies the centripetal force requirement to allow the inward acceleration that is characteristic of circular motion.
3) I understand everything that I read.
4) We did not talk about how the total amount of mechanical energy of a satellite in elliptical motion remains constant. Since the only force doing work upon the satellite is an internal (conservative) force, the work done by external forces is zero and mechanical energy is conserved. Unlike the case of circular motion, the energy of a satellite in elliptical motion will change forms. The force of gravity does work upon a satellite to slow it down as it moves away from the earth and to speed it up as it moves towards the earth. If the speed is changing, the kinetic energy will also be changing.